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lfunc_lfunctions • Show schema
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{'Lhash': '1099788039970759216948655227246', 'a10': [26.166822153470818, 0], 'a2': [-2.616682215347082, 4.532226544243032], 'a3': [0, 0], 'a4': [-9.694051632227424, -16.790589958213904], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-16.509020225533515, 28.59446181380625], 'a8': [59.598094557270095, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '90053585461296031942891244068', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.616682215347082, -4.532226544243032], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [16.509020225533515, -28.59446181380625], [-171.5, -297.04671349806245]], [[1.0, 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'9.347475936847739707514818970492087', '10.34322161539012132995111103223186', '10.62618071158525917884677460958408'], 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.055555555555555566, 'root_number': '0.98480775301220805936674302458952301367064325171984241879 + 0.1736481776669303488517166267693147960003756771840693872*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.027777777777777776', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.867579788762575429703371294669', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.48934643509059807346059533151', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.61724473018249549790943511883', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/w/136/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-405-9.7-c3-0-22', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.027777777777777783, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.867579788762575429703371294669', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1099788039970759216948655227246', 'Lhash_array': ['1099788039970759216948655227246'], 'label': '2-405-9.7-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/w/136/1'}